The strong Lefschetz property of Gorenstein algebras generated by relative invariants (Q6583740)

The problem of determining Artinian Gorenstein algebras which have the strong Lefschetz property has been intensively studied. The authors consider Artinian Gorenstein algebras generated by the relative invariants of prehomogeneous vector spaces of commutative parabolic type. Determinants, determinants of symmetric matrices, and Pfaffians of alternating matrices of even size are some of the polynomials which belong to this family. They prove that these algebras have the strong Lefschetz property. The key ingredient in their study is the theory of generalized Verma modules of Lie algebras.